Solving the first inequality for x we get:
[tex]\begin{gathered} 4x+4>-32, \\ 4x+4-4>-32-4, \\ 4x>-36, \\ \frac{4x}{4}>-\frac{36}{4}, \\ x>-9. \end{gathered}[/tex]
Solving the second inequality for x we get:
[tex]\begin{gathered} 16>4x+4, \\ 16-4>4x+4-4, \\ 12>4x, \\ \frac{12}{4}>\frac{4x}{4}, \\ 3>x\text{.} \end{gathered}[/tex]
Therefore, the solution set is:
[tex]-\inftyThe graph of the solution set is
the entire number line, as shown below:
